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Xiangyu Zhou

Publications and source records attributed to Xiangyu Zhou.

At least 55 records · Page 3Linked to original sources
arXiv2024

Exploring The Neural Burden In Pruned Models: An Insight Inspired By Neuroscience

Vision Transformer and its variants have been adopted in many visual tasks due to their powerful capabilities, which also bring significant challenges in computation and storage. Consequently, researchers have introduced various compression methods in recent years, among which the pruning techniques are widely used to remove a significant fraction of the network. Therefore, these methods can reduce significant percent of the FLOPs, but often lead to a decrease in model performance. To investigate the underlying causes, we focus on the pruning methods specifically belonging to the pruning-during-training category, then drew inspiration from neuroscience and propose a new concept for artificial neural network models named Neural Burden. We investigate its impact in the model pruning process, and subsequently explore a simple yet effective approach to mitigate the decline in model performance, which can be applied to any pruning-during-training technique. Extensive experiments indicate that the neural burden phenomenon indeed exists, and show the potential of our method. We hope that our findings can provide valuable insights for future research. Code will be made publicly available after this paper is published.

cs.NE↗
arXiv2024

Monge-Ampère type equation on compact Hermitian manifolds

Given a cohomology $(1,1)$-class $\{β\}$ of compact Hermitian manifold $(X,ω)$ possessing a bounded potential and fixed a model potential $ϕ$, motivated by Darvas-Di Nezza-Lu and Li-Wang-Zhou's work, we show that degenerate complex Monge-Ampère equation $(β+dd^c φ)^n=e^{λφ}μ$ has a unique solution in the relative full mass class $\mathcal{E}(X,β,ϕ)$, where $μ$ is a non-pluripolar measure on $X$ and $λ\geq0$ is a fixed constant. As an application, we give an explicit description of Lelong numbers of elements in $\mathcal{E}(X,β,ϕ)$ which generalized a theorem of Darvas-Di Nezza-Lu in the Hermitian context.

math.DG↗
arXiv2024

Optimal $L^2$ Extensions of Openness Type

We study the following optimal $L^2$ extension problem of openness type: given a complex manifold $M$, a closed subvariety $S\subset M$ and a holomorphic vector bundle $E\rightarrow M$, for any $L^2$ holomorphic section $f$ defined on some open neighborhood $U$ of $S$, find an $L^2$ holomorphic section $F$ on $M$ such that $F|_S = f|_S$, and the $L^2$ norm of $F$ on $M$ is optimally controlled by the $L^2$ norm of $f$ on $U$. Answering the above problem, we prove an optimal $L^2$ extension theorem of openness type on weakly pseudoconvex Kähler manifolds, which generalizes a couple of known results on such a problem. Moreover, we prove a product property for certain minimal $L^2$ extensions and give an alternative proof to a version of the above $L^2$ extension theorem. We also present some applications to the usual optimal $L^2$ extension problem and the equality part of Suita's conjecture.

math.CV↗
arXiv2024

Multiplier Submodule Sheaves and a problem of Lempert

In this article, we establish an $L^2$ extension theorem for Nakano semi-positive singular Hermitian metrics on holomorphic vector bundles, and the strong openness and stability properties of the multiplier submodule sheaves associated to Nakano semi-positive singular Hermitian metrics on holomorphic vector bundles. We solve affirmatively a question of Lempert on the preservation of Nakano semi-positivity under limit of an increasing metrics based on Deng-Ning-Wang-Zhou's characterization of Nakano positivity.

math.CV↗
arXiv2024

On the subadditivity of generalized Kodaira dimensions

The goals of this paper are of two aspects. Firstly, we introduce the notion of generalized numerical Kodaira dimension with multiplier ideal sheaf and establish the subadditivity inequalities in terms of this notion, which can be used to give an analytic proof of O. Fujino's result on the subadditivity of the log Kodaira dimensions. Secondly, motivated by Zhou-Zhu's subadditivity of generalized Kodaira dimensions, we adopt another definition of generalized Kodaira dimension with multiplier ideal sheaf and show they are equal by using Okounkov bodies. As one application, we show that the superadditivity part in Zhou-Zhu's setting also holds true. As another application, we give an alternative proof of Zhou-Zhu's subadditivity formula, in the case when the singular metric $h_L$ has analytic singularities, by using generalized Iitaka fibrations.

math.CV↗
arXiv2024

A Le Potier-type isomorphism twisted with multiplier submodule sheaves

In this paper, we obtain a Le Potier-type isomorphism theorem twisted with multiplier submodule sheaves, which relates a holomorphic vector bundle endowed with a strongly Nakano semipositive singular Hermitian metric to the tautological line bundle with the induced metric. As applications, we obtain a Kollár-type injectivity theorem, a Nadel-type vanishing theorem, and a singular holomorphic Morse inequality for holomorphic vector bundles and so on.

math.CV↗
arXiv2024

On the Range of a class of Complex Monge-Ampère operators on compact Hermitian manifolds

Let $(X,ω)$ be a compact Hermitian manifold of complex dimension $n$. Let $β$ be a smooth real closed $(1,1)$ form such that there exists a function $ρ\in \mbox{PSH}(X,β)\cap L^{\infty}(X)$. We study the range of the complex non-pluripolar Monge-Ampère operator $\langle(β+dd^c\cdot)^n\rangle$ on weighted Monge-Ampère energy classes on $X$. In particular, when $ρ$ is assumed to be continuous, we give a complete characterization of the range of the complex Monge-Ampère operator on the class $\mathcal E(X,β)$, which is the class of all $φ\in \mbox{PSH}(X,β)$ with full Monge-Ampère mass, i.e. $\int_X\langle (β+dd^cφ)^n\rangle=\int_Xβ^n$.

math.CV↗
arXiv2023

Efficient Bottom-Up Synthesis for Programs with Local Variables

We propose a new synthesis algorithm that can efficiently search programs with local variables (e.g., those introduced by lambdas). Prior bottom-up synthesis algorithms are not able to evaluate programs with free local variables, and therefore cannot effectively reduce the search space of such programs (e.g., using standard observational equivalence reduction techniques), making synthesis slow. Our algorithm can reduce the space of programs with local variables. The key idea, dubbed lifted interpretation, is to lift up the program interpretation process, from evaluating one program at a time to simultaneously evaluating all programs from a grammar. Lifted interpretation provides a mechanism to systematically enumerate all binding contexts for local variables, thereby enabling us to evaluate and reduce the space of programs with local variables. Our ideas are instantiated in the domain of web automation. The resulting tool, Arborist, can automate a significantly broader range of challenging tasks more efficiently than state-of-the-art techniques including WebRobot and Helena.

cs.PL↗
arXiv2023

CR eigenvalue estimate and Kohn-Rossi cohomology

Let $X$ be a compact connected CR manifold with a transversal CR $S^1$-action of real dimension $2n-1$, which is only assumed to be weakly pseudoconvex. Let $\Box_b$ be the $\overline{\partial}_b$-Laplacian, with respect to a $T$-rigid Hermitian metric (see Definition 3.2 of $T$-rigid Hermitian metric). Eigenvalue estimate of $\Box_b$ is a fundamental issue both in CR geometry and analysis. In this paper, we are able to obtain a sharp estimate of the number of eigenvalues smaller than or equal to $λ$ of $\Box_b$ acting on the $m$-th Fourier components of smooth $(n-1,q)$-forms on $X$, where $m\in \mathbb{Z}_+$ and $q=0,1,\cdots, n-1$. Here the sharp means the growth order with respect to $m$ is sharp. In particular, when $λ=0$, we obtain the asymptotic estimate of the growth for $m$-th Fourier components $H^{n-1,q}_{b,m}(X)$ of $H^{n-1,q}_b(X)$ as $m \rightarrow +\infty$. Furthermore, we establish a Serre type duality theorem for Fourier components of Kohn-Rossi cohomology which is of independent interest. As a byproduct, the asymptotic growth of the dimensions of the Fourier components $H^{0,q}_{b,-m}(X)$ for $ m\in \mathbb{Z}_+$ is established. We also give appilcations of our main results, including Morse type inequalities, asymptotic Riemann-Roch type theorem, Grauert-Riemenscheider type criterion, and an orbifold version of our main results which provides an answer towards a folklore open problem informed to us by Hsiao.

math.CV↗
arXiv2023

Approximation and extension of Hermitian metrics on holomorphic vector bundles over Stein manifolds

We show that a singular Hermitian metric on a holomorphic vector bundle over a Stein manifold which is negative in the sense of Griffiths (resp. Nakano) can be approximated by a sequence of smooth Hermitian metrics with the same curvature negativity. We also show that a smooth Hermitian metric on a holomorphic vector bundle over a Stein manifold restricted to a submanifold which is negative in the sense of Griffiths (resp. Nakano) can be extended to the whole bundle with the same curvature negativity.

math.CV↗
arXiv2023

A note on Demailly's transcendental Morse inequalities conjecture

Let $(X,ω)$ be an $n$-dimensional compact Hermitian manifold with $ω$ a pluriclosed Hermitian metric, i.e. $dd^cω=0$. Let $\{α\},\{β\}\in H^{1,1}_{BC}(X,\mathbb R)$ be two nef classes, such that $α^n-nα^{n-1}\cdotβ>0$. In this short note, we prove that if there is a bounded quasi-plurisubharmonic potential $ρ$, such that $α+dd^cρ\geq 0$ in the weak sense of currents, then the class $\{α-β\}$ contains a Kähler current. This gives a partial solution of Demailly's transcendental Morse inequalities conjecture.

math.CV↗
arXiv2023

On a Bogomolov type vanishing theorem

Let $X$ be a compact Kähler manifold and $(L,h)\rightarrow X$ be a pseudoeffective line bundle, such that the curvature $iΘ_{L,h}\geq 0$ in the sense of currents. The main result of the present paper is that $H^n(X,\mathcal{O}(Ω^p_X\otimes L)\otimes \mathcal{I}(h))=0$ for $p\geq n-nd(L,h)+1$. This is a generalization of Bogomolov's vanishing theorem.

math.CV↗
arXiv2023

DGP-Net: Dense Graph Prototype Network for Few-Shot SAR Target Recognition

The inevitable feature deviation of synthetic aperture radar (SAR) image due to the special imaging principle (depression angle variation) leads to poor recognition accuracy, especially in few-shot learning (FSL). To deal with this problem, we propose a dense graph prototype network (DGP-Net) to eliminate the feature deviation by learning potential features, and classify by learning feature distribution. The role of the prototype in this model is to solve the problem of large distance between congeneric samples taken due to the contingency of single sampling in FSL, and enhance the robustness of the model. Experimental results on the MSTAR dataset show that the DGP-Net has good classification results for SAR images with different depression angles and the recognition accuracy of it is higher than typical FSL methods.

cs.CV↗
arXiv2022

Linear isometric invariants of bounded domains

We introduce two new conditions for bounded domains, namely $A^p$-completeness and boundary blow down type, and show that, for two bounded domains $D_1$ and $D_2$ that are $A^p$-complete and not of boundary blow down type, if there exists a linear isometry from $A^p(D_1)$ to $A^{p}(D_2)$ for some real number $p>0$ with $p\neq $ even integers, then $D_1$ and $D_2$ must be holomorphically equivalent, where for a domain $D$, $A^p(D)$ denotes the space of $L^p$ holomorphic functions on $D$.

math.CV↗
arXiv2022

Achievement of 200,000 hours of operation at KEK 7-GeV electron 4-GeV positron injector linac

KEK electron positron injector LINAC initiated the injection operation into Photon Factory (PF) light source in 1982. Since then for 39 years, it has served for multiple projects, namely, TRISTAN, PF-AR, KEKB, and SuperKEKB. Its total operation time has accumulated 200 thousand hours on May 7, 2020. We are extremely proud of the achievement following continuous efforts by our seniors. The construction of the injector LINAC started in 1978, and it was commissioned for PF with 2.5 GeV electron in 1982. In parallel, the positron generator linac was constructed for the TRISTAN collider project. The slow positron facility was also commissioned in 1992. After the KEKB asymmetric-energy collider project was commissioned in 1998 with direct energy injections, the techniques such as two-bunch acceleration and simultaneous injection were developed. As the soft structure design of the LINAC was too weak against the great east Japan earthquake, it took three years to recover. Then the construction and commissioning for the SuperKEKB project went on, and the simultaneous top-up injection into four storage rings contributes to the both elementary particle physics and photon science.

physics.acc-ph↗
arXiv2022

Synthesizing Analytical SQL Queries from Computation Demonstration

Analytical SQL is widely used in modern database applications and data analysis. However, its partitioning and grouping operators are challenging for novice users. Unfortunately, programming by example, shown effective on standard SQL, are less attractive because examples for analytical queries are more laborious to solve by hand. To make demonstrations easier to create, we designed a new end-user specification, programming by computation demonstration, that allows the user to demonstrate the task using a (possibly incomplete) cell-level computation trace. This specification is exploited in a new abstraction-based synthesis algorithm to prove that a partially formed query cannot be completed to satisfy the specification, allowing us to prune the search space. We implemented our approach in a tool named Sickle and tested it on 80 real-world analytical SQL tasks. Results show that even from small demonstrations, Sickle can solve 76 tasks, in 12.8 seconds on average, while the prior approaches can solve only 60 tasks and are on average 22.5x slower. Our user study with 13 participants reveals that our specification increases user efficiency and confidence on challenging tasks.

cs.PL↗
arXiv2021

On the extension of Kähler currents on compact Kähler manifolds: holomorphic retraction case

In the present paper, we show that given a compact Kähler manifold $(X,ω)$ with a Kähler metric $ω$, and a complex submanifold $V\subset X$ of positive dimension, if $V$ has a holomorphic retraction structure in $X$, then any quasi-plurisubharmonic function $φ$ on $V$ such that $ω|_V+\sqrt{-1}\partial\bar\partialφ\geq \varepsilonω|_V$ with $\varepsilon>0$ can be extended to a quasi-plurisubharmonic function $Φ$ on $X$, such that $ω+\sqrt{-1}\partial\bar\partial Φ\geq \varepsilon'ω$ for some $\varepsilon'>0$. This is an improvement of results in \cite{WZ20}. Examples satisfying the assumption that there exists a holomorphic retraction structure contain product manifolds, thus contains many compact Kähler manifolds which are not necessarily projective.

math.CV↗